The NomadBSD-image can be tricky to upgrade to FreeBSD 13.1 because the layout on the disk is lean and optimized for maximum user-space.
So I experienced problems upgrading a vanilla NomadBSD 130R-20210508 on a 16 GB USB-stick. It ran out of disk-space on /ROOT/ and choked.
During upgrade the old 13.0 kernel is kept and renamed to /boot/kernel.old. But you can change this behaviour (and instead delete the old kernel during upgrade) in freebsd-update.conf - and that gives the system juuust enough disk-space to complete the upgrade.
So before running freebsd-update, you have to open the freebsd-update.conf (with root privileges)
> sudo vim /etc/freebsd-update.conf
and (near the bottom) uncomment and change the line # BackupKernel yes to:
BackupKernel no
or simply use this command:
sudo sed -i.old 's/# BackupKernel yes/BackupKernel no/' /etc/freebsd-update.conf
Happy upgrading 
Please chime in with corrections and addition